## Thursday, June 30, 2011

### Solutions to Introduction to Basic Physics, Part 22

We now examine the solutions for the problems in Part 22, on series and parallel circuits.

1)Two resistances of 20 ohms and 5 ohms are connected in parallel by a student. He then connects this combination in series with a 3 ohm resistance and a battery of 1 ohm resistance.

a) Draw a conventional diagram of the circuit (i.e. not in Wheatstone Bridge format).

b) Find the resistance of the resistors in parallel.

c) Find the total resistance of the circuit.

The circuit diagram is shown above, labelled for 'Problem 1'.

b) The resistance of the 2 resistors, 20 ohms and 5 ohms, in parallel is easily found from the total for the special case of two resistors in parallel:

R = R1 R2 / (R1 + R2) = (20 0hms)(5 ohms) / 25 ohms = 100 ohms^2/25 ohms

R = 4 ohms

c) The total resistance for all contributors in series is just the sum:

4 ohms + 3 ohms + 1 ohm = 8 ohms

2) The photo shows a sketch of a Wheatstone Bridge Circuit at Harrison College, to be used to find the resistances of two resistors (R1 and R2) connected as shown, with two differing positions of the galvanometer. The total resistance R is also to be taken.

A student using the diagram finds his voltmeter reads 1.0 V and the total resistance is 4 ohms when the slide wire is at the end position noted.

If the balance for obtaining G = 0 (e.g. galvanometer reading zero) is the intermediate position, and the slide wire is then at 45 cm, find the values of R1 and R2.

The total resistance from the end position (100 cm) = 4 ohms. We know from the photo that the two resistors R1 and R2 are connected in series so that:

R1 + R2 = 4 ohms

We are given the first position of the slide wire as L1 = 45 cm, then:

R1/ 4 ohms = 45 cm/ 100 cm

and: R1 = 0.45 (4 ohms) = 1.8 ohms

Then:

R2 = 4 ohms - 1.8 ohms = 2.2 ohms

3) A resistance R2 is connected in parallel with a resistance R1. What resistance R3 must be connected in series with the combination of R1 and R2 so that the equivalent resistance is equal to the resistance R1? Draw a circuit diagram of the arrangement.

We let R1 = r and let R2 = 2r.

These are in parallel so the total resistance for them is:

R(T) = R1 R2/ (R1 + R2) = r(2r)/ (r + 2r) = 2r^2/ 3r = 2r/3

We require that the total resistance in series be such that the equivalent resistance is equal to the resistance R1, or r.

Thus, we require:

R3 + 2r/3 = r

and, solving by algebra:

R3 = r - 2r/3 = r/3

The circuit diagram is shown, labelled as 'Prob. 3'.

4) Three equal resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 10 watts. (Note: Power = V x I, voltage x current).

What power would be dissipated if the three resistors were connected in parallel across the same potential difference?

You need to bear in mind that for the case in parallel the current is divvied up, e.g. total current I = I1 + I2 + I3. Since all the resistors are equal (call each r ohms) and the voltage is the same then the power for the parallel case would be one third the power for the series case, or 10/3 Watts.

### Another Overpaid 'Dick' and Asshole: Mark Halperin

Let me say off the bat, I can't stand Mark Halperin, the overpaid hack asshole who writes a weekly column for TIME and an MSNBC "senior political analyst". I think the guy is a smug, hyper-entitled, narcissistic little piece of sewage and a know-nothing twerp from the corporate echo chamber who has no business analyzing anything....except maybe doog poop specimens.

Be that as it may, my estimation of this putz reached even new lows this morning, while watching MSNBC's Morning Joe when the little dick said about President Obama (see also my previous blog applauding Obama's fiery stance yesterday):

"I thought he was a dick yesterday,"

So evidently this hack-dick didn't like what Obama said, in terms of his (for once) fiery demeanor to try to get the intransigent Repukes to cooperate in a debt ceiling solution. This, as opposed to letting the fuckers roll him, as they did with last year's tax cut extension deal.

But hey, what's new? Most of the corporate media axis including many in the alleged "liberal domains" of the WaPo and NY Times, like their Dem presidents mellow...usually too mellow...and never, ever acting or talking as fighters. For these collective dicks, populism of any kind is terrifying and brings images to mind of people with torches and pitchforks fighting the elites for a small piece of pie....like we now see in Greece and in England.

In this regard, the pusillanimous Halperin somewhat resembles one late alleged "dean of the Washington Press corps" by the name of David Broder who used to write for the Washington Post. He too brayed loudly whenever a Dem showed a minuscule bit of spunk and fight. But say one thing, say the next, at least Broder possessed an IQ above room temperature, unlike the smirky Halperin! At least Broder wrote with some flair and a modicum of gravitas when he issued his injunctions to moderation.

Meanwhile, we hear Halperin has apologized for his Obama slur, and has been "suspended indefinitely." Scarborough blamed a producer for not hitting the delay button, instead of ... blaming the person who actually said it. But then Scarborough is another overpaid dick and the only person worth watching on his show (or hearing) is his co-host Mika Brzezinski.

What Halperin ought to have done, if he was going to use any slur starting with d at all (as in dickheads) was to aim it at the disgusting Republicans who adamantly refuse to broker a deficit reduction deal that includes taxes. Thus, they are acting the part of sociopaths.

Hopefully, Halperin's juvenile outburst will impel Mr. Obama to even greater forcefulness in the coming weeks in his battles with Republicans.

### A Stirring Press Conference, Mr. Obama! Now, stand strong!

I was finally elated to see some fire in the belly of Mr. Obama at his press conference. His eyes flared, and he aimed emotional daggers at the obstructing repukes - who remain foursquare against raising any revenues as part of deficit reduction. But as I've repeatedly shown, any sane person or group would know we can't get to \$2.4 trillion in deficit reduction by cutting spending alone! As one British economist noted, quoted in The Economist: "Saying you can improve the economy by just cutting taxes is like saying you can run faster by cutting off a foot!"

So true! But why don't the Republicans get it, and cooperate for a true, beneficial deal for this country? Well, because they've all signed "pledges" (compliments of Grover Norquist) not to. If any ONE of them breaks from the pack, there'll be hell to pay and not only will Norquist go ballistic, but all the other Rs will lose it as well - probably even more than my bro over me denying him his "loan" some days ago. (At least in his mind, I actually didn't!)

This obstinacy and perverse obstructionism, refusal to genuinely cooperate, puts the Dems and Mr. Obama in a hellacious bind. As calamitous as a default would likely be, giving in to crazed, spending cut frenzied repukes would be much worse. Bank on it! If the Ds cave on this extortion, and give in to allow ALL spending cuts with few or no tax hikes, then as I showed a few blogs ago it will mean the implosion of the economy (due to 40-50% reduction in aggregate demand) and plausibly 18% unemployment by next summer. This will be an unmitigated catastrophe for the Democrats and Mr. Obama - especially with the general election only months away - but the Republicans will be in 7th heaven. They will have effectively gotten the Dems and the President to cooperate in the destruction of the economy to advance the Repukes' own partisan political agenda. It means that what transpired in November last year, that election debacle, will be like a 'tea party' compared to what will occur next November!

In effect, what this means is that Mr. Obama (like Mr. Clinton also facing the repukes over a gov't shutdown 16 years ago) must choose the lesser of two evils. As incredible (or appalling) as it may sound, this means he must not merely use rhetoric - even charged rhetoric - but be fully prepared to take the Repukes to the wire, and - if it means allowing a default- then he must do it! He cannot allow himself to submit - or the nation to submit- to this vicious blackmail by the rethugs, to this fiscal "gun" to the nation's head. (To use blogger Andrew Sullivan's turn of phrase).

The polling figures are on Mr. Obama's side, as only 8% believe he's responsible for the debt impasse and problems. What people are thus looking for, is bold and unintimidated leadership such as Bill Clinton displayed when he stood up to similar Repug extortion threats (from Gingrich & Co.) on his watch. Then the government actually did shut down, at least temporarily. Clinton never blinked, Gingrich and the repukes did. The same must play out this time, no exceptions. Under NO circumstances must Obama blink, or he will look like a rook, a newbe, a callow former state Senator ...and an easy mark for all further dealings (including the extension of the horrific Bush tax cuts in 2012, an election year!)

The bottom line: Obama cannot and must not go along with the Republicans in their insane, economy-destroyng spending cut orgy! Any give-in here can only be a Pyrrhic victory, at unaceptable cost and far worse than any bond pirates might threaten! If it means default, so be it. We must also stop hearing ANYTHING, any mild words from the Ds circulating in the media, to the effect that even smacks of Repuglican-memes and narratives. Thus, Max Baucus must be made to shut up about "Medicare cuts" (which plays into the Repuke dynamic) just as Joe Lieberman in his courting of Tom Coburn to try and elicit \$600b in such cuts. Obama needs to repeatedly remind these cheese eaters that his own Affordable Health Plan incorporates \$500b in Medicare cuts and so this is already the solution.

Meanwhile, Mr. Obama himself must cease his own tax cut pandering, especially after last December's extension of the Bush tax cuts. That means ceasing forthwith any more talk of another year of "payroll tax cuts". No, no, no and NO! As an article in MONEY magazine noted, the benefits from the existing payroll tax freeze have only been marginal and consumers continue to be defensive in their spending. One year of such a freeze was bad enough as it denied badly needed money to support Social Security and Medicare. TWO years would be a freaking catastrophe and play right into Repuke memes that both are approaching insolvency and lacking money! By adding an additional year of payroll tax freezing, Mr. Obama would abet this, so even if he wants it congress must turn it down. (At least the still D-held Senate).

We will wait to see what occurs, but I want to see not just strong rhetoric but action driven by spine...plain old-fashioned intestinal fortitude as opposed to another capitulation. That means taking the Republicans to the cliff and beyond, if need be, in order not to destroy this nation's economy! As I said...the lesser of two evils.

### Latest Climate News: NOT Sanguine!

One of the claims often made by what I call the flat Earth or climate change denier brigade, is that volcanic emissions dwarf human fossil fuel or other related activity (e.g felling rain forests) in terms of producing CO2. This canard has now been fairly well shattered with the recent publication of a paper, Volcanic Versus Anthropogenic Carbon Dioxide in the journal Eos: Transactions of the American Geophysical Union( Vol. 92, No. 24, June 14, 2011, p. 201).

The essential data of the paper is shown in the accompanying graph, for which the dots show a time series of the anthropogenic carbon dioxide CO2 multiplier (ACM) calculated from time series data on anthopogenic CO2 emission rates and Marty & Tolstikhin's (1998) study of preferred volcanic emission rates. In their paper appearing in Chemical Geology (Vol. 145, p. 233) the latter authors gave a preferred estimate of 0.26 gigaton per year for present day global volcanic emission rate and injection. Their study encompassed CO2 emissions from divergent tectonic plates, intraplates (plumes) and convergent plates - e.g. displaying volcanism.

Moreover as the current Eos paper observes, their computations "assessed the highest preferred minimum and maximum global estimates, making them appropriate high end volcanic limits for the comparisons with anthropenic CO2 emissions covered with in this article".

To that extent, the Eos author (Terry Gerlach of the U.S. Geological Survey)showed from his time series that the projected anthropogenic CO2 emission rate of 35 gigatons per year is 135 times greater than the 0.26 gigatons per year emission rate for volcanoes, plumes etc. This ratio of 135:1 (anthropogenic to volcanic CO2) is what defines the anthropogenic multiplier, an index of anthropogenic CO2's dominance over volcanic inputs.

Supporting Gerlach's 2010 projection and ACM data, is the just announced word - from Thomas Karl of The National Climate Data Center (see: The Denver Post), June 29, p. 4) that in their 'Annual State of the Climate Report for 2010', that year was "tied with 2005 as the warmest on record". According to Director Karl: "The indicators show, unequivocally, that the world continues to warm."

Meanwhile, the Eos paper puts the final nails in the coffin of the "volcanoes did it" excuse! It is also worth mentioning how the ACM data show an astounding rise in the CO2 multiplier from about 18 in 1900, to roughly 38 in 1950, which parallels the vastly enhanced use of automobiles as a primary mode of personal transport - with the planet now saddled with nearly 600 million vehicles! Every manjack in a third world nation even seeks to own one!

Interestingly the only volcanic event which even came close to human emissions was the eruption of Mt. Pinatubo in the Philippines in 1992. It generated CO2 emission rates roughly between 0.001 and 0.006 gigaton per hour, or closely approximating to the 0.004 gigaton anthropogenic per hour (e.g. based on 35 gigatons per year).Thus, as the Eos article observes:

For a few hours individual volcanoes may emit as much or more CO2 than human activities. But volcanic emissions are ephemeral while anthropogenic CO2 is emitted relentlessly from from ubiquitous sources..

Which means human activity is a vastly more significant source of CO2 and the major reason we are approaching a CO2 concentration (taken to be from 550- 600 ppm)that marks the threshold to the runaway greenhouse effect.

Let us hope humans are smart enough to get the message and act on it before it's too late!

## Wednesday, June 29, 2011

### Introducing Basic Physics (Series & Parallel Circuits)- Pt. 22

We now look at series and parallel circuits using the Wheatstone Bridge method. The same set up is used as shown in the photo for Part 21 and the circuit diagram (for the slide wire set up) is in Fig. 1. The separate circuit diagrams are shown in the accompanying diagrams (Fig. 2a and 2b)for the series and parallel cases.

Apparatus used:

i) Wheatstone Bridge

ii) d.c. voltmeter (0- 3 V)

iii) ammeter (0- 1A, 0- 10A)

iv) sensitive galvanometer

v) low voltage d.c. source (2V or under)

vi) wires for connections

Main Background points:

1. Series Circuits.

The general diagram is such as shown in Fig. 2(a). Here, separate components are connected in such a way the source of emf (battery) forces electric current through all components (e.g. resistors) in sequence. Once steady conditions are established the same current flows through all resistances. The total resistance is the sum of the individuals:

R = R1 + R2 + R3 + ........R_n

where R1, R2 are the resistances of the separate resistors.

The voltage in a series circuit is such that each component causes a drop in potential and the sum of all potential drops is equal to the emf applied to the total circuit:

E = V1 + V2 + V3 + ......V_n

Current in a series circuit is constant so the total is the same flowing through any given component:

I = I1 = I2 = I3 etc.

2. Parallel circuits

This set-up is such as shown in Fig. 2(b). In parallel circuits the current paths branch, hence are not sequential. Since several paths are available for current flow instead of just one, then the total resistance is less than the resistance of any ONE of the alternative paths, or resistors. The total is:

1/R = 1/R1 + 1/R2 + 1/ R3 + .....1/R_n

Thus, the reciprocal of the total resistance of a parallel circuit is just the sum of the reciprocals of the separate resistances.

Special case:

This is for two in parallel, which makes easy computation for the total:

E.g.

1/R = 1/R1 + 1/R2 = R1 + R2 / (R1 R2)

Then: R = (R1 R2)/ (R1 + R2)

The voltage in a parallel circuit is the same across any component of the circuit, as it is across the circuit as a whole, so:

E = V1 = V2 = V3 etc.

The current in a parallel circuit is the sum of all the currents flowing in the separate components, i.e.

I = I1 + I2 + I3..+

Procedures for experiment

A) Series circuit.

Use the Wheatstone Briddge slide wire set up (Fig. 1) to determine the resistance of each resistor and use an emf no larger than 1.0 V. Connect all resistors in series and first measure the total resistance with Wheatstone Bridge (R_T). Connect ammeter and voltmeter across each as indicated (Fig. 2(a)) to obtain resistance based on Ohm's law, R= V/I)

B) Parallel circuit.

Use the same Wheatstone Bridge, but now connecting all the resistors in parallel using the resistance board (see, e.g. the left side of the photograph in Part 21 of the set up). Use the voltmeter and ammeter to take all necessary readings as per Part (A) but now with Rs in parallel. Take care in selection of meter readings so accurate readings will be obtained (preferably to three signficant figures).

Practical Problem:

A student at Harrison College uses the Wheatstone Bridge method to connect up resistors in parallel analogous to Fig. 2(b) He uses his ammeter and voltmeter (0- 1V) to obtain the following readings.

For R1: I1 = 0.50 A, V1 = 0.75 V

For R2: I2 = 0.25 A, V2 = 0.75 V

For R3: I3 = 0.75 A, V2 = 0.75V

a) Find the individual resistances based on his measurements.

b) Find the total resistance.

Solution:

a) Using Ohm's law, one obtains:

R1 = V1/ I1 = 0.75V/ 0.50A = 1.50 ohms

R2 = V2/ I2 = 0.75V/0.25A = 3.0 ohms

R3 = V3/I3 = 0.75V/ 0.75A = 1.0 ohms

b) The total for resistors in parallel:

1/R = 1/ R1 + 1/R2 + 1/ R3

1/R = 1/ 1.5 + 1/3 + 1/1

1/R = 1/(3/2) + 1/3 + 1 = 2/3 + 1/3 + 1 = 2

So: R = 1/2 = 0.5 ohms

Check: Is this smaller than any of the individual values? Yes!

Other Problems:

1)Two resistances of 20 ohms and 5 ohms are connected in parallel by a student. He then connects this combination in series with a 3 ohm resistance and a battery of 1 ohm resistance.

a) Draw a conventional diagram of the circuit (i.e. not in Wheatstone Bridge format).

b) Find the resistance of the resistors in parallel.

c) Find the total resistance of the circuit.

2) The photo shows a sketch of a Wheatstone Bridge Circuit at Harrison College, to be used to find the resistances of two resistors (R1 and R2) connected as shown, with two differing positions of the galvanometer. The total resistance R is also to be taken.

A student using the diagram finds his voltmeter reads 1.0 V and the total resistance is 4 ohms when the slide wire is at the end position noted.

If the balance for obtaining G = 0 (e.g. galvanometer reading zero) is the intermediate position, and the slide wire is then at 45 cm, find the values of R1 and R2.

3) A resistance R2 is connected in parallel with a resistance R1. What resistance R3 must be connected in series with the combination of R1 and R2 so that the equivalent resistance is equal to the resistance R1? Draw a circuit diagram of the arrangement.

4) Three equal resistors are connected in series. When a certain potential difference is applied across the combination, the total power dissipated is 10 watts. (Note: Power = V x I, voltage x current).

What power would be dissipated if the three resistors were connected in parallel across the same potential difference?

## Tuesday, June 28, 2011

### How the GOP Could Destroy the Economy by Massive Spending Cuts

As President Obama begins more negotiations with the GOP's stalwarts on the handling of the debt ceiling increase, he needs to bear in mind (and take to heart) Sen. Bernie Sanders recent exhortations to "stand tall" and refuse to make any quick and easy deals to avoid confrontation. Sanders then referred to the tax reform dealings back last fall, and how Obama got gamed by the repukes. He can't let that happen this time around, as his re-election may well hinge on him showing the determined leadership a President is supposed to have. Obama's no longer a lowly state senator, and he needs to act the part. Also, he can't be afraid to piss people off, even the Repuglicans!

The Rethuglicans' bad faith is the problem at heart. If they have all signed "pledges" not to raise taxes,,ever, then Obama's hands are putatively bound in the making of ANY deficit reduction deal! He simply cannot be seen to give in to one-sided demands, nor to lopsided demands! The burdens must be shared between higher revenue (taxes) and spending cuts, not all on the latter, or even four-fifths. (Some ideas circulating have increased taxes at \$400b, but spending cuts more than \$1.6 b. This is nonsense and insane! It must be at least HALF and HALF! Also why I refuse to give any more \$\$ to the DSCC or any other Dem organizations until I see some evidence of spine. So far I don't!)

Anyway, an essay to read carefully is the recent one entitled Our Greek Tragedy, appearing in TIME (July 4, p.. 26) by Rana Forhoohar. She writes in one segment that I advise all Repug followers to read:

"There's still a belief that the government can cut spending wholesale and expect consumers to pick up the slack. This is magical thinking!"

Indeed, it is! The reason is that the Republicans in their grossly stubborn behavior, don't appreciate or understand the economic concept of aggregate demand. It is the index of aggregate demand that ultimately determines investment potential, and also unemployment and whether an economy is "paralyzed" - as ours seems to be (as disclosed by the constant references of pundits).

Aggregate demand is composed of two parts: 1) demand generated by consumers for goods and services, and 2) the demand for investment goods. When the level of aggregate demand is high, both these components are generally equally high, and the levels of production and employment are high. On the other hand, when aggregate demand is low - or even one of the components (e.g. (1)) is VERY low, then levels of production and employment plummet. Right now we are seeing a tabulated rate of 9% unemployment and more like 16% real unemployment which is signaling that the aggregate demand is low. In addition, we see almost no movement of corporate dollars (now nearing two trillion) to invest in labor or labor infrastructure - to enable more workers to be hired. Thus, also low demand for labor investment goods.

The two are clearly feeding on each other.

Now, the next thing, why is consumer demand still low, falling almost quarterly? It is because the wages that support it are low! The average workers' wages have remained static or gone down since the recession theoretically ended. Thus, consumers are buying less, and resorting to unusual savings devices (like extreme coupon clipping) when they do buy! Also, when people eat out now they're more likely to get meal coupons off Groupon.com then go to the cheapest place that takes them, and after eating ding the business by leaving zero tip.

In other words, the demand side of the landscape looks so poorly for consumers they are hunkering down...likely expecting another shoe to drop. That "shoe" - when they pay attention to the news, sounds like a severe cut in possible social services, thanks to the Republicans' rhetoric. If they foresee such cuts, say even for Medicaid for sick granny or Uncle Tim, then they will pull back on spending in case they will need the money to help care for them! Ditto with seniors on Medicare, if they suspect cuts are in the works (as Sen. Max Baucus has intimated). Thus, they also pull back on their spending, or even going out to eat, say at Bob Evans.

The total effect is to put more jobs (at those places, services) under pressure, and possibly engender more job loss. Thus, the mere mention of the GOP mammoth (~ \$2 trillion)spending cuts puts consumers under such potential threat that they already psychologically act as if it's happening. Meanwhile, nothing is being said forcefully (even by the nominal opposition) to defend higher taxes and revenues that would save programs - Pell Grants, Medicare, Medicaid, environmental laws...or whatever.

The word is even leaking out that the Repukes want spending on water regulation cut, meaning an epidemic of cryptosporidium - such as struck Milwaukee in 1994- could easily occur again!

Meanwhile, investor demand for investment goods is largely hinging on their optimism or not. If investors are pessimistic (as many are now...because of the volatility of stocks) then they will withhold their investments.

Here's a numerical example of how this all works. Assume we have "full employment" (e.g. 4%) and it generates a total of \$1,000 worth goods and services in a day. This is also the sum total of the profits and incomes the employees and employers share. Let households comprised of workers and employers use a large fraction (e.g. 90% or \$900) of their income to purchase goods and services for consumption. The remaining 10% or \$100 is saved but eventually purchased by investors as investment goods.

Now, say an agent or effect appears (e.g. states cutting pensions and benefits) which causes consumers to pull back on their spending such that the \$1,000 becomes \$900. Then, with an income of only \$900, the consumption is also reduced, say to only \$800. \$200 in "savings" accrues but inveestors are so pessimistic and traumatized by the consumption decline that they only purchase \$50 of the \$200. In this case, the aggregate demand has shrunk 15% from \$1000 (\$900 consumption + \$100 investment) to \$850 (\$800 consumption + \$50 investment).

In this way, the stage is setting up for a major financial disaster, and a new recession or even depression.

Let's say at this point (as shown above) spending cuts -mammoth ones - are now imposed by a derelict government which thinks it can get a handle on deficits almost solely via cutting. Then, consumers will pull back even further and incomes will drop to the 50% level or \$500. They will still spend \$450 on necessities, and investors will not budge from their \$50 investments. The total of aggregate demand is now \$500 (\$450 + \$50) or 50% of the original. But because of the contraction there is no accumulation of inventory (unsold goods) even as services such as bars & restaurants go out of business for lack of clientele (after all, only 50% of the original income is now available!) We do see a kind of equilibrium restored, but because production is now at only 50% of the full employment level, unemployment is now 50%.

As a comparison, the maximum unemployment in the Great Depression hit 35%. The above scenario played out on the national stage for next year, shows a projected net loss of aggregate demand in the neighborhood of 40-50% if the Repukes get their way before Aug. 2nd and \$2 trillion in nothing but spending cuts is used to "solve" the deficit and enable the debt ceiling to be raised. This translates into an unemployment level of more than 18% this time next year (30% real unemployment) and a new recession bordering on depression. Think the repukes will be happy? Hell, they'll be having wet dreams at the prospect of such an abomination (which they deliberately created) within months of the general election.

THIS is what we face if the Republicans get their way, and no taxes are a significant part of a deficit reduction package. This is why Obama has to finally take off the kid gloves and put on the brass knuckles! He's fighting as much for his own 2nd term as he is for the nation! That means not taking any repuke shit, but rather dishing it out to them! Acting "Grownup"? Hell, grown-ups don't allow themselves to be pushed around by 2-bit punks with an attitude.

### "Disowned” for denying a “loan”? So Be it!

Some ten months ago I blogged about my second brother “Donnie” (pseudonym) and his gambling problem – actually an addiction- and the serious problem of giving money away to him, when you know damned well it’s enabling his habits. I called this a moral hazard. See, e.g.

http://brane-space.blogspot.com/2010/09/of-brothers-and-moral-hazards.html

To recap briefly,I told him to find something constructive to do, or anything - that would keep his mind occupied and away from slots. I also told him that given his already known heart problems, he needed to knock off ALL smoking. I informed him that I certainly couldn’t or wouldn’t be subsidizing his ill health problems brought on by his bad habits, nor should he expect me to. He was now a “big boy” (62 years old)and needed to take charge of his life, as opposed to endlessly copping for handouts to support his smoking, gambling, or pure laziness. As I pointed out to him, he’s getting \$2200 a month for doing absolutely nothing, and others are busting their humps across the nation, often working TWO scut jobs and not earning near as much as he receives gratis from the gov't. So, there was NO excuse to graft for money, especially from siblings who have their own financial issues and budgets to deal with.

At that time, after begging for \$40 over the phone for something, and my refusal, he let loose a stream of expletives and asserted he “disowned” me. However, a couple of months later the relationship was tentatively repaired (at least nominally) and I sent him a Xmas gift of \$20 (which in hindsight I perhaps ought not have done, but I’d hoped he’d see the difference between receiving a gift and a “loan”). I told him I no longer give loans because I never receive them back! A point reinforced in a recent issue of MONEY magazine, wherein their finance advisor said under no circumstances give out family loans unless specific conditions are met, including: setting a repayment deadline date, interest -if any- to be paid if deadline is missed. Since I knew none of this would wash with Donnie, I declined all loans to him period, but left the room open for gifts. Obviously, the latter would only occur at most twice a year: for his birthday and Xmas!

Sure enough, in late May he returned asking for a “loan” of \$25. Again, I made it clear to him I no longer give loans, period. However, I would give him a \$25 gift for his 63rd birthday (on June 9th). I figured this would be the end of it until Xmas but I was fooling myself. Anyway, soon thereafter he suffered an apparent heart attack and was told by the doctors to shape up (again stop smoking) and the best thing would be to have open heart surgery right there and then – as they suspected major blockage. Donnie declined, fearing such surgery and opting instead for an expensive Plavix regimen which also required catching taxicabs to purchase it at distant private pharmacies, at high cost (according to his version). I told him a more practical solution to his problems was simply to get the operation.

Now, rejecting the latter was a choice he made. A deliberate choice. Knowing he has limited finances, or so he claims(though he does have VA benefits!), and also trots out other reasons why he "must eat out and not cook", must take cabs everywhere - not buses, can't save money etc., WHY choose the most expensive heart health path? Just where the hell do you think you are going to get the money? DO you think you can endlessly tap family, brothers, forever?

So two weeks ago he wrote and asked to borrow \$50 for “cab fare” to go and have his blockage scan appointment. This is now \$75 asked for in the span of about a month! For five days I deliberated over this, swinging back and forth between whether this was another load of codswallop (designed to provoke sympathy and get money to buy smokes or gamble) or whether it was for real. After two more days of thrashing it out, I opted to write him in a short letter: “You can have this \$50, not as a loan, but outright – provided this is the last time you ask for any money”. I also asked him to put it in writing, then I'd send the money.

Two days after that, I received a letter from him, but not in reply to the one I sent (because that would have been too rapid). This letter automatically assumed there’d be no money coming and let loose a barrage of hate and vitriol that caught me by surprise, and had my wife shaking her head as she read it. My first reaction was, Who the bloody fuck does this little shit think he is? Does he believe he's entitled to my money? How dare the little fuck launch into a venomous tirade including 'burning forever in hell' merely because I declined to gratify his wishes (at that time, though as noted I did send a letter offering the \$ but with strings). As for my wife, her immediate response was:

“THIS is your brother?”she asked. “All you did is turn him down for a loan!

I replied that I didn’t even do that, since I offered him the money but with one major string attached, never to ask again! However, he decided to attack me and spit in my face, before even getting it! I posted two segments to show some of the hostility in the letter, which I will use to make a point (Note: most of his letter was omitted because I wouldn’t put the content on a public blog. I put these sections on because they're relevant to my arguments. Also, if anyone at anytime sends me anything, I consider it fair game for my blogging – especially if what they send has drastic negative connotations, displays an openly hateful or vitriolic attitude or whatever. Be sure you know what the hell you’re doing before sending me anything, especially material that can be scanned and published! I regard everything sent to me in my personal domain, for personal use - howsoever I see fit!)

As to his letter(any other names redacted to protect those he involves), note his first words are: ‘Hey X-Brother!’ (He doesn't even know the appropriate form is 'Ex-Brother')

But in truth and fact Donnie has never been a brother. Oh, he is by blood, but he lacks the emotional wiring to relate as anything other than a perpetual snake oil salesman, con artist, beggar and grafter. Looking back all through the years at about a dozen contacts he initiated (as opposed to me) at least ten of them were purely to graft for money, or beg. He begins letters cordially enough, but then doesn’t even waste one more paragraph before the money begging commences – and it’s always for a “loan” despite the fact he’s never paid them back. (I take that back. He did “pay one \$150 loan back” from ten years or so ago, by giving me a set of laminated 19980s baseball and football cards). So obviously, loans have no meaning for him.

Note also from the letter the sense of absolute entitlement. He feels – by his words and attitude- he’s fucking entitled to MY money! Note the violent reaction is almost as if I was the one who had ROBBED HIM of \$50, when all I did(in his mind) was decline to give it to him. (But again, I had written him to make arrangements to give it provided he agreed to no more asking at all in the future)

Thus, his whole reaction – including the ‘burn in Hell” bullshit at the end, is totally out of proportion to the stimulus of a perceived rejection!

Then, the accusations of being “cheap” are priceless, as is his woefully wrong perception that \$50 is nothing much. In fact, some people almost kill themselves in tough manual jobs to earn that in one day! Think of Florida’s sugar cane cutters. So, what he is really assuming is that parting with \$50 is nothing, no big deal for me.

“Cheap”? Only an purblind, half-monkey idiot would believe that judiciously managing one’s expenses, cash outflows is “cheap”. The sad thing is he isn’t capable of doing it himself. Money is “cheap” to him because he disrespects it (e.g. "you can't even give me a lousy fifty bucks" on p. 2), and uses it as if it has no value. He pisses it away senselessly on smokes, slots or whatever…then expects others to bail his sorry ass out when he exhausts the greenbacks. Then, when others who manage their money deny him the use of theirs to piss away, he loses his composure and unleashes a barrage of hate. Showing, of course, he was never a true brother to begin with, but a pathological hollow man or cipher: a pretender, user, manipulator and exploiter merely sharing the same surname.

His other bellyaching about his funeral and “advanced directives” is also choice. The sad fact is that Donnie’s choices are totally setting him up to die alone, by himself, and in a pauper’s grave. And with NO one there to see him off..

But in the end, that will have been his choice, as it was his uncle David’s – another guy (my dad’s younger brother) who could never handle money, never use it properly and was hostage to alcohol and gambling addictions. I can still recall when he came around our home in Milwaukee in 1954 and stayed a few days, before he started begging for money "to find a job downtown", and came in drunk late one night. Dad asked him to leave the next morning, since there was no place for a drunkard with five young kids in the house. He never returned and died some years later, of alcohol poisoning.

"Donnie" in a similar way has already left whatever family he once had, and he did it by his own choice, as David actually did. As for those who say I ought not write about “family”, sorry! When they ask for it, and act in certain ways, there are no holds barred. If they don’t wish to be blogged about, then they shouldn’t send vitriolic letters through the mail. Especially when they ensure they can never see my replies (e.g. by sending my letter back without reading). "Family" is too often a cover to do whatever, use emotional extortion and get away with every and any thing (or invoke as a pretext to let others, fellow siblings etc. get away with anything!). To me, family means a constellation of people who can relate to you, who often have your back (and don't talk behind your back!) and may or may not be blood relations. I have a rather large extended family (over 255 people), thanks to my wife's huge clan, as well as a long time friend of 40 years. I know in a pinch I can count on any of them to have my back - and not stab me in the back! In the end, that's what real family is about! Not the extent to which selfish demands can be appeased at the drop of a hat - at the beck and call of an unreconstructed, overaged sibling brat!

## Monday, June 27, 2011

### Solutions to Part 21 (Electric circuits)

We now undertake the solutions for the problems in Part 21, Introducing Basic Physics: Simple electric circuits. The problem will be given then the solution.

1) A 12 V battery has an internal resistance of 2 ohms. If it is connected in series with a voltmeter and another resistance R = 4 ohms, what would the voltmeter read? What would an ammeter read placed in the same circuit?

The circuit set-up is shown for Problem (1). We first need to find the ammeter reading:

I = E/ (R + r) = 12V /(4 ohms + 2 ohms)= 12V/ 6 ohms = 2 A

Then the voltmeter (V) reading may be obtained from Ohm's law for the circuit:

V = I(R) = 2A (4 ohms) = 8V (at the position indicated)

This may also be validated by use of:

V = E - Ir = 12V - (2A)(2 ohms) = 12V - 4V = 8V

(e.g. 4V of total emf is lost through the source)

2) A Wheatstone Bridge circuit is connected as shown in Fig. 1(b). The galvanometer is found to read zero when point C is located exactly midway along a wire 1m in length (e.g. connecting A and B in the diagram). A known resistance coil R is used which is made of copper (rho = 1.72 x 10^-8 ohm-m) and is 50 m long, wound tightly in a coil.

a) If the cross sectional area A = Ï€r^2 and r = 0.001m, find the value of R(x).

The experimental circuit is shown for Problem 2, with L1 and L2 denoting the respective lengths.

We first need to obtain the known resistance, but this must be done using the resistivity of the wire that's given (rho = 1.72 x 10^-8 ohm-m) in conjunction with the resistance as a function of resistivity eqn.

R = rho(L)/A = rho(L)/ Ï€r^2

R = (rho = 1.72 x 10^-8 ohm-m)(50m)/(Ï€ x.001m^2) = 0.27 ohms

And, from the Wheatstone Bridge set up:

R(x)/ R = L1/L2

But since: L1 = L2 = 50 cm, then:

R(x) = R (L1/L2) = R (1) = 0.27 ohms

b) If a new resistor R made up of 100m length of the same copper wire is then used, then how must the lengths L1 and L2 change to achieve a galvanometer reading of zero?

We assume the only change made is to R, and R(x) is still 0.27 ohms. Then only the lengths L1, L2 will vary.

The new known resistance, call it R' = rho(2L)/A = 2R = 0.54 ohms

(since 100m = 2(50m))

Then:

R(x)/ R' = L1/ L2 = 0.27 ohms/ 0.54 ohms = 0.5

So: L1 = 0.5 (L2) or L2 = 2L1

The total length is 1m, so:

L1 + L2 = 100 cm

substituting for L2 (2L1):

L1 + 2L1 = 3L1 = 100 cm and L1 = 100cm/ 3 = 33.3 cm

So: L2 = 100 cm - L1 = 100cm - 33.3 cm = 66.7 cm

### Two Million More Reasons to Soak the Rich!

William Bonner, aka "Billy the Kid", was a loathsome scumball, one of the worst vermin to inhabit the West. Before he was gunned down (by Pat Garrett) he had one of several last photos taken about 130 years ago in which is called "tintype" today. The photos, slightly larger than modern baseball cards, should all have found their way into sewers or dumpsters by now, but one actually made its way to a Denver Auction.

There it was purchased....get this... for TWO MILLION DOLLARS! This sent waves of absolute revulsion through me, when I considered what that sum of money could otherwise have accomplished...how much good it could have done... as opposed to pissing it away for the 130-year old image of a rat. For example:

- Paid twenty secondary school teachers' salaries for two years

- Paid forty school librarians' salaries for 4 years (many school librarians are now being laid off across the nation as states come to grips with budget woes)

- Paid for health care, and needed (overdue) medical treatments for one thousand homelesss adults.

- Purchased six months worth of nutritious meals for 100 homeless kids.

- Enabled construction of a 40-room shelter for homeless families.

But what was the money used for? To purchase a little tintype photo of one of the worst villains of the Old West!

Later word has it that the purchaser was one of the billionaire Koch brothers. The same Koch brothers who use their other extra, excess monies to fund the Tea Party's exploits. (Though most Tea Baggers don't have clue one who's behind their agenda!)

It is now time, given that they have so much EXTRA, unneeded money to piss away, to tax the bastards to the hilt! That's why I now propose increasing the marginal tax rate at the top to what it was during the Eisenhower years: 91%. Also, bring back the estate taxes and put all kinds of provisos on them (i.e. no gifting beforehand to family members, trusts etc.) to ensure all gets paid to Uncle Sam.

Anytime a rich guy can just piss so much way discloses he has excess money, in fact more than he reasonable knows what to do with....or NEEDS. I make the same claim for the Koch bro that purchased the Billy the Kid photo, as I do for the other rich dude that paid \$6 million (at an auction sponsored by Debbie Reynolds) for the dress Marilyn Monroe wore (when the subway draft blew it up around her waist) in 'Seven Year Itch' (1955) and the other character that tossed out \$1.8 million for Michael Jackson's favorite jacket.

All this money wastage shows the rich have way too much...as well as time on their hands.

Of course, with the repukes in power, and now yammering incessantly to give the richest even BIGGER tax cuts (while they take Medicare from poor seniors and replace it with useless vouchers), we will have to expect even more obscene purchases that will only make normal humans wince at the chutzpah, arrogance and depraved flaunting. This is the Republicans' plan: to give each rich millionaire another Lexus each year in tax cut equivalents, and each billionaire enough to purchase a new Lear jet.....or maybe....the last photo ever taken of Adolf Hitler before heading into his Berlin bunker as the Russians approached.

I am sure the next billionaire who buys that will have much to share in common with the subject!

## Sunday, June 26, 2011

### Introduction to Basic Physics (Electric Circuits) Pt. 21

In this instalment we begin the examination and investigation of simple electric circuits, starting with some basic rules and principles and very simple experiments to determine the resistance, R, in a circuit. There are two methods that can be used one I call "simple", otherwise known as the ammeter-voltmeter method, and the other which is more complex (shown in Fig. 1(b). The latter actual practical set up is also shown in Fig. 2.

Generally, at Harrison College, we employed the simple A-V method for the introductory physics students in the 3rd form (equivalent to the U.S. 9th grade) and used the Wheatstone Bridge method for the Upper fifth form (equivalent to the U.S. 12th grader, or HS senior). Thus, by the time the Barbadian physics student arrives at his senior year he's already been well exposed to simple electric circuits, and knows how to set up both series and parallel circuits (which we will see in the next instalment).

Some Basics:

1.Ohm's Law:

In effect, this is what the student is really seeking to show in the experiment:

I = V/R

where I is the current (in amperes) and V the voltage in volts, while R is the resistance in ohms. In terms of the units then:

Amperes (or 'amps') = Volts/ Ohms

2. Internal Resistance

Technically speaking, every battery, or source of emf (electro-motive force) also has an internal resistance, r. Thus, the theoretical emf (E-t) will always be larger than the actual, measured emf,E. And hence also, any terminal voltage in the circuit (call it V(ab)) will be less than E. Thus:

V(ab)= E - Ir

or, if an additional resistance R is connected:

E - Ir = IR, or

I = E / (R + r)

The fine points of (2) are usually not introduced until the upper fifth form.

3. Resistivity

This features prominently when lengths of resistance wire come into play and hence the resistance will change depending on the length. If rho denotes resistivity of a material, e.g. metal wire, and the wire is L feet long, then the resistance R (in ohms) is:

R = rho (L)/ A

where A is the cross-sectional area of the wire.

Again, (3) is a consideration usually left until the more advanced levels.

I. Ohm's Law by the Simple Method

The student is issued an ammeter (with letter I adjacent, for current) to measure the amperes, and a voltmeter (with E adjacent) to denote volts or emf at that point, and a set of 5 unknown or test resistors, as well as a battery or other emf source.

For each test resistor inserted, the student records the voltage and current in volts and amps, then obtains the resistance using:

R = E/ I = V/I

At the end of the experiment the student is given the actual resistor values which he must compare with the empirical or test values he found, and then estimate the percentage error for each.

II. Wheatstone Bridge Method:

This circuit is connected as shown in diagram Fig. 1(b). In this case, the unknown resistance R(x) is wired in as shown. The instrument denoted by (G) is a galvanometer. The known resistance is denoted R, and the student adjusts or moves a clip along a length of wire from A to B yielding different lengths L1 and L2. At specific points where 'C' is located on AB, the galvanometer will read 0 (N.B. the value R should be chosen before hand so that point C falls on the middle third of AB when G reads zero).

Practical example:

In performing the Ohm's law experiment (to find an unknown resistance R(x)) a student at Harrison College makes the following measurements:

Length AC = 35 cm

Length CB = 65 cm

R = 5 ohms

G = 0

Using this data, find the value of R(x):

Solution:

R(x) / R = (AC)/ (BC)

R(x)/ 5 ohms = 35/65 = 7/13

Therefore: R(x) = 5 ohms (7/13) = 2.7 ohms

Problems:

1) A 12 V battery has an internal resistance of 2 ohms. If it is connected in series with a voltmeter and another resistance R = 4 ohms, what would the voltmeter read? What would an ammeter read placed in the same circuit?

2) A Wheatstone Bridge circuit is connected as shown in Fig. 1(b). The galvanometer is found to read zero when point C is located exactly midway along a wire 1m in length (e.g. connecting A and B in the diagram). A known resistance coil R is used which is made of copper (rho = 1.72 x 10^-8 ohm-m) and is 50 m long, wound tightly in a coil.

a) If the cross sectional area A = Ï€r^2 and r = 0.001m, find the value of R(x).

b) If a new resistor R made up of 100m length of the same copper wire is then used, then how must the lengths L1 and L2 change to achieve a galvanometer reading of zero?

### Why Jason Lisle is wrong in his Solar Super-granulation Polarity finding

Jason Lisle, in his Ph.D. dissertation ('Probing the Dynamics of Solar Supergranulation and its Interaction with Magnetism'), makes the claim that by using Michelson Doppler Imager (MDI) velocity data (from the SOHO spacecraft) in concert with local correlation tracking techniques, he was able to develop adequate "refinements" in the latter and thereby excavate enough signal to ascertain a "persistent N-S alignment" which is taken to be a polarity preference associated with the supergranules. As I intend to show, this conclusion is suspect and doesn't hold up when the foundational assumptions (and error techniques) are examined more closely.

One thing any solar researcher or worker ought to be able to relate to, and to concede, is the ever present trap of selection effects. These can often creep into an investigation even conducted with the best intents. As an example, in my (1980-86) investigations of the origin of SID flares associated with certain active regions, an early conclusion was that the most geo-effective (i.e. able to disrupt terrestrial communications, or cause the most intense sudden ionospheric disturbances) were associated with the most rapidly growing and magnetically complex sunspots. (Fig. 1). These were typically the largest delta -class spots with numerous magnetic polarity intrusions (e.g. one magnetic polarity intruding deeply into another causing large magnetic field gradients).

However, on performing a deeper analysis which included cross-referencing all SIDs to all optical flares (of all classes) appearing on all available H-alpha films (e.g. over all Carrington rotations in 1980) and validated via the x-ray signatures from the SMS-GOES satellite) it was found this was a premature conclusion. Indeed, contrary to the overall rubric that only large area, delta spot- populated ARs spawned powerful SIDs (and hence associated SID flares) I found that nearly 35% of all major SID flares (which generated the largest SID effects) were associated with optical subflares. (Solar Phys., Vol. 92, p. 259). In other words, the counter-intuitive finding was that just over one-third of the largest SID flares arose from the smallest energy optical flares (typically 10^21 J ). A test of the sampling errors using the coefficient of determination confirmed this.

I point this out because very early in his dissertation (p. 17), Lisle concedes an inability to properly resolve granules via his MDI data, though he does make an appeal to local correlation tracking (LCT) as a kind of savior since it allows motions to be deduced from the images even when individual moving elements aren't well resolved. (I.e. the granules are the individual elements or units of supergranules). The question that arises, of course, is whether the product of such LCT manipulation is real, or to put it another way, an objective physical feature that is not associated with instrumental effects, distortions or errors.

Exacerbating this suspicion is Lisle's own admission (ibid.) that LCT "suffers from a number of artifacts". One thing any worker in the field ought to know is that any time an artifact appears, however it does so, it's time to put on the warning radar. (Lisle evidently does this but as I will show, this isn't enough).In Lisle's case the warning is sounded by the emergence of a "large-scale, disk centered convergence anomaly". He notes this is due to a selection effect on granules and the anomaly can be mitigated by further treatment.

This is normally attainable, but again, removal of scale selection effects depends on the scale of the anomaly- especially in relation to the sought after signal. In my SID flare studies at a particular scale, it appeared that solar spicules in the vicinity of large, delta-spot penumbra were scenes of emergence of optical subflares that spawned major SIDs. But when all the incidents of these correlated spicules were assembled, then subjected to a Fourier analysis (and compared with velocity field and vector magnetogram data) the signal vanished. Evidently, aberrantly bright spicules (in the centerline) were erroneously recorded as optical subflares though they were nearly 10-15 x less in energy. (Correction could be made when the spectrum was observed in the wings, which disclosed darkness). In this sense, the anomaly manifested itself as a much diminished signature which appeared more energetic than the actually sought signal, while in Lisle's case, the anomaly was already much larger than the sought signal scale (by about ten times). In their Astrophysical Journal paper (Vol. 608, p. 1170), 'Persistent North-South Alignment of the Supergranulation', Lisle, Rast and Toomre assert that:

supergranular locations have a tendency to align along columns parallel to the solar rotation axis.... this alignment is more apparent in some data cubes than others

They also add: The alignment is not clearly seen in any single divergence image from the time series of this region (Figs. 1a–1b) but can be detected when all 192 images comprising that series are averaged

This also ought to have raised some suspicions as to whether it is really a spurious signal emerging in the series averages. For example, an averaging of SID-flare intensity data would show that the original (spurious) conclusion I gave above was the appropriate one, i.e. "only large area, delta spot- populated ARs spawned powerful SIDs (and hence asociated SID flares)"

Going back to the same Ap.J. paper, the authors write:

The anisotropy observed in the time-averaged image of Figure 1c is not a property of the individual supergranules but is instead due to a weak positional alignment, producing vertical striping with nearly the same horizontal length scale as the supergranulation itself.

The north-south alignment of the solar supergranulation is observed only after long temporal averages of the flow. After 8 days of averaging, the striping is quite strong, while shorter averaging times show the effect less well.

In Figure 3a, s[x], s[y] , and their ratio s[x]/s[y] are plotted as a function of averaging time. The plots show the average value obtained from two independent well-striped 15 deg x 15 deg equatorial subregions of the data set

In the above, s[x], s{y] refer to the rms or root mean square errors.

Now, the key link to the persistence of the "polarity" alignment as the authors put it:

" s[x]/s[y] shows a smooth transition from values near one at low averaging times to values exceeding 2.5 for the full time series. This increase reflects the slow decrease in x compared to y due to the underlying longitudinal alignment of the evolving flow. The random contributions of individual supergranules to s[x] or s[y] scale as 1/(Nl)^½, where Nl is the number of supergranular lifetimes spanned over the averaging period. Vertical striping of the average image emerges visually when the averaging time exceeds the supergranular lifetime by an amount sufficient to ensure that the contribution of the individual supergranules falls below that of the long-lived organized pattern. The slowly increasing value of s[x]/s[y] at very long averaging times suggests that the underlying organization is persistent in time, with a lifetime > or = 8 days.

The underscored segment above is critical, since Lisle in his dissertation refers to a "false flow" whenever his larger tile size includes more granules. In effect, an additional flow anomaly has been engendered because of the effects of including larger boxes (usually 5 pixels by 5 pixels) which have more granules. This is in addition to the large central convergence artifact. Which brings us to the use of the asymmetrical outcomes for the rms error ratio: s[x]/s[y] upon which the conclusion of persistence appears to rest, i.e. from the authors' foregoing description, which is also based on Lisle's dissertation - but which one is prevented from extensively quoting from (owing to copyright restrictions!) Hmmm...wonder why?

Anyway, the use of the error ratio s[x]/s[y] as a "rosetta stone" to uncover this "persistence" of pattern can't really be justified, and it's a pity that the referees of the Ap. J. paper didn't see this - but then my own original Solar Physics paper had to be referred to more capable statistics-trained referees because the first one couldn't handle it!

Without wishing to make this overly long, I refer readers to the excellent paper by James G. Booth and James P. Hobert ('Standard Errors of Prediction in Generalized Linear Mixed Models', appearing in The Journal of the American Statistical Association (Vol. 93, No. 441, March 1998, p. 262) in which it is noted that standard errors of prediction including use of rms errors, and ratios thereof are "clearly inappropriate in parametric models for non-normal responses". This certainly appears to apply to Lisle et al's polarity "model" given the presence of significant "false flows" and "large convergence artifacts" (the latter with 10 times the scale size of the sought signal). The authors meanwhile recommend instead a conditional mean-squared error of prediction which they then describe at great length. They assert that their methods allows for a "positive correction that accounts for the sampling variability of parameter estimates".

In Lisle et al's case, the parameters would include the propagation speed of supergranule alignments, after their s[x]/s[y] is replaced by the rubric offered by the J. Am. Stat. Soc. authors, including the computation of statistical moments (p. 266) to account for all anisotropies and other anomalies which appear.

Until this is done, it cannot be said that there exists any "persistent alignment" in the solar supergranulation! Sorry, boys...and Ap.J. refs, and editors!

## Saturday, June 25, 2011

### Solutions to compound lens problems

Problems from Pt. 20:

(1) A telephoto lens consists of a converging lens of focal length 6 cm placed 4 cm in front of a diverging lens of focal length (-2.5 cm).

a) Do a graphical construction of the system showing where the image would be.
b) Compare the size of the image formed by this combination with the size of the image that would be formed by the positive lens alone.
-----------

Solutions:

a) The graphical constuction is shown in the accompanying diagram, showing the image is 10 cm from the optical axis of the diverging lens. If the negative (diverging ) lens had not been used then the image AB would have been formed at the principal focal plane of the +6 cm (converging) lens, 6 cm from it. However, the diverging lens decreases the convergence of the rays (left side) refracted by the converging lens and causes them to focus at A'B', 14 cm from the converging lens - and 10cm from the diverging lens, as shown.

b) The image AB that would have been formed by the converging lens alone is (6 cm - 4 cm) = 2 cm beyond the f = (-2.5 cm) lens and is taken as the virtual object for that lens. ThenL s1 = -2 cm, and:

1/s1' = 1/f - 1/s1 = 1/ (-2.5) - 1/(-2) = -1/2.5 + 1/2 = 1/10

Then: s1' = 10 cm

Thus, the final image A'B' is real and 10 cm beyond the divergin lens - as the graphical construction shows.

The linear magnification: M1 = (-s1'/ s1) = (10 cm/ 2 cm) = 5

and since, h'/h = 5, then h' = 5h so the image formed by the combination is 5x larger than that formed by the (+) lens alone.

2) The objective lens of an astronomical telescope has a focal length of 6 ft. The eyepiece has a focal length of 2 inches.

a) Find the angular magnification that the telescope will produce when used for distant objects.

b) A rule for observing extended astronomical objects, such as planets or nebulae, is that the telescope magnification should not exceed 60x per inch of objective aperture.
----

Solutions:

(a) M = F/ f(e) where F = 6' = 72" and f(e) = 2"

Then: M = 72"/ 2" = 36 x

(b) It is not possible to strictly assert the condition is met (since no aperture is provided) but given the long focal length (6') it is more likley the aperture is at least 6" so the condition is easily met. (60x per in. would be 360x. Even a 1" aperture would easily meet the condition, however.)

If the astronomical telescope of this problem is used to observe the planet Jupiter,is the condition met or not? If not, what focal length eyepiece is needed to get the maximum angular magnification?
---

Soln.

Assuming a 6" aperture to get 360x for Jupiter then we'd need: M= 360 and

f(e) = F/M = 72"/360 = 1/5"

3) The objective of a telescope has a focal length F = 30 in. When it is used for an object at a great distance, then the distance between the objective and eyepiece is 32 in. What is the angular magnification?

In this case, the focal length of the eyepiece f(e) = 32 in. - 30 in. = 2 in.

We have: M = F/ f(e) = 30 in./ 2 in. = 15 x

## Friday, June 24, 2011

### "Uncle Tom" Sowell - Another pie-eyed Economic Idiot!

I was enjoying my breakfast of freshly brewed coffee along with a fancy bear claw this morning, when all of a sudden I turned the page of our local rag to find another incompetent load of economic drivel from "Uncle Tom" Sowell staring at me. I nearly dropped my coffee all over the paper (which might have been better) on reading some of his moronic codswallop which shows he hasn't the faintest clue about the Pareto Distribution, or Pareto Efficiency - which I covered in two previous blogs.

Since I've dealt with the noisome and dishonest Uncle Tom before, let me merely stick to his more outrageous claims in this particular column. He writes, for example:

"They (American seniors) want their Social Security and their Medicare to stay the way they are- and their anger is directed against those who want to change the financial arrangements that pay for these benefits"

Now that's a really neat euphemism, "change the financial arrangements"! But as I already showed, the "change in financial arrangements" these miscreants want for Medicare is NO Medicare! Paul Ryan's pseudo -Medicare plan essentially converts the whole system into a voucher system. The senior will be handed a \$12,000 voucher (if that) then be sent on his or her merry way to try and purchase a policy on his or her own. Good luck on that! I tried it, in perfect health, merely 3 years ago, and the BEST policy I was offered was one with an \$8,500 deductible (which didn't cover all medical issues) and for \$450 a month. A senior in poor health would be lucky to get anything! The reason is the medical loss ratio for the insurance company would be too excessive, no profits! The senior could as well kill herself, or...do what one enterprising senior recently did in NC, rob a bank (sticking up a teller for \$1) in order to be jailed and receive health care there. (No one could make this shit up, believe me!)

THIS is what the great Ryan "financial arrangement" will mean for most poor or sickly elderly. The CBO itself estimates that out of pocket costs will rise to 67% of totals, compare to about 25% now for standard Medicare.

As for Social Security, their idea of "financial arrangements" is to put the money into the stock market or what they call "privatizing it". Just what do these genii think would have happened had Bushie jr. gotten his way in 2005, and Social Security had been privatized? Well, seeing now in hindsight the stock market crash in the fall of '08, most seniors would be eating cat food out on the streets- assuming they could find spare cans in enough dumpsters!

Sowell obviously doesn't know dick or diddly, or he is simply too dishonest to come out with the real facts.

He then bloviates:

"Their anger should be directed at those politicians who were irresponsible enough to set up those programs without putting aside enough money to pay for the promises that were made- promises that cannot now be kept"

More nitwit bollocks! In fact, when FDR set up Social Security (read the history of this in the excellent book Social Security and Its Enemies by Max J. Skidmore) he knew the ONLY practical way to make social insurance feasible was to implement it as a payment system via current workers to current retirees. NO other way would work. This was known by ALL from the outset, and also that it would be paid for by payroll taxes. Thus, Sowell is disingenuous in asserting they didn't put aside money to pay for it. In fact, the payroll taxes accumulated as the implementers knew they would, and built up huge cash reserves! (Even more was infused in 1983, after Alan Greenspan proposed a higher payroll tax, to the current 6.2%, to take into account the coming baby boomer onslaught).

The problem? Despicable politicos and pork mongers have raided it to disguise the size of deficits, starting with Reagan. Thus, the money was there, but stolen! Hence, it is ignorant and wrong to say "promises were made that couldn't be kept". Indeed, as recently as 2004 more than \$3.3 trillion remained in S.S. Trust funds (which DO exist and are kept in special bonds) but that has been drawn down by the protracted military adventures, occupations (see my previous blogs)

As for Medicare, that was also designed to be paid for by payroll taxes and it did have the money to sustain it. But idiot Sowell doesn't mention (or mayhap he forgets) the changes that caused its monies to bring it to near insolvency:

i) Not allowing Medicare from the outset to bargain for lowest prescription drug prices like the VA does.

ii) Not keeping a tighter rein on Medicare fraud.

iii) the 2003 Bush Medicare Act which created "Medicare Advantage" plans that consume \$12 billion more per year than standard Medicare

All those in concert have placed Medicare near insolvency, but that problem can be reversed - not by killing Medicare like Ryan wishes - but reversing all the above policies: e.g. telling the Big PhrmA to go get fucked and allowing bargaining like the VA, eliminating all Medicare fraud, and eliminating all Medicare Advantage plans.

In addition, raising payroll taxes another 1 % wouldn't hurt, and increasing the payroll cap to at least \$1 million, would also help sustain it.

Thus, Sowell's rejoinder to the effect "Don't you understand the money is not there any more? is pure B.S. It was there, but was raided by filthy political thieves and collaborators! (E.g. lobbyists)

The last bit of bullshit is the worst:

"..The way Social Security was set up was so financially shaky that anyone who set up a similar retirement scheme in the private sector would be sent to prison for fraud"

Again, this shows what a disreputable fraud he is! In fact, Social Security was never set up as a "retirement scheme", it was set up as a social insurance program. In the way it pays for current retirees, it is exactly like social insurance programs in other countries. For example, the National Insurance program of Barbados uses the exact same approach, and it started before FDR's. A certain % is taken out of the worker's pay each period and this goes to pay current retirees.

As for American Social Security, social insurance, as Max Skimore notes (op. cit.) it was always made clear to retirees that Social Security was to be but ONE prop of their retirement income, not the whole enchilada! They were expected to supplement it by pensions from private sources, or other means (e.g. annuities). Funny that a nabob like Sowell can't even communicate that simple truth about the program - but then, knowing his dishonest stance, maybe he prefers not to! It's easier to call it a "retirement scheme" analogous to a privately run operation.

As for tossing old ladies off of cliffs, no matter what changes are proposed for future retirees (i.e. the current Gen X and Y'ers) if they sow a lack of confidence in the system, such that these current workers lose faith in the programs, then that will impact all current beneficiaries negatively - if only by brazen political acts to reduce their S.S. COLAS while increasing the cost of Medicare premiums.

Why wouldn't Uncle Tom know that? Who knows? Maybe those who take his words as "gospel" ought to inquire!

### GOP Tax Position: Dishonest, Despicable ....Traitorous!

"Let me be clear! Tax hikes are OFF the table!"

So said House Speaker John Boehner on Thursday, confirming again the GOP's bargaining position from bad faith in terms of raising the nation's debt ceiling, since they are prepared to reject ab initio the ONE solution that would most easily and rapidly solve our problems! This shows the GOP, aka repukes, are not serious about deficit control, but only wish to exploit it as a means of extortion on the Democrats to cut long-term social programs. (Ironically, at the same time, the GOP refuses to entertain any significant military spending cuts!)

This brash posturing comes on the heels of a non-partisan Congressional Budget Office (CBO) report on Wednesday, outlining a projected "explosion" in government spending. The CBO names Social Security and Medicare, but let's be frank about what's really going on here. We need the perceptions of deep politics for this, not superficial or pundit-cheap politics such as on the tube.

The population has more than tripled in the U.S. since FDR initiated the Social Security program, and more than doubled since LBJ initiated Medicare (in 1966) and so basic arithmetic stands at the foundation of most the increase. In addition, it was a Republican president, Richard M. Nixon, who approved the go ahead for cost of living (COLA) increases in Social Security, realizing if this wasn't done, then rising medical expenses and fees from Medicare would soon swallow ALL of a retiree's money.

The real basis then for the "explosion" of government costs is NOT Social Security and Medicare per se, but the unwillingness to fund them! (While simultaneously raiding Social Security monies to pay for military adventures and pork to hide the size of deficits!)

The Republicans have known all along that if enough tax cuts and expensive military interventions, occupations could be mounted, the government would eventually spend down its assets and reach the point where the social programs would be in jeopardy- unless drastically pared back. The GOP and anti-tax terrorist Grover Norquist (who designed an insane "pledge" against raising taxes that all new Goop-ers must sign) have succeeded in achieving this condition by:

- ten years of military occupations at a total cost now of nearly \$3.4 trillion

- ten years of Bush tax cuts at a cost of over \$3.1 trillion (including the last extension in December), and

- increasing the defense budget to 3.9% of GDP in 2004 (which former defense analyist Chuck Spinney called "the start of a war on Social Security and Medicare")

Thus, the "ballooning costs" of Social Security and Medicare as reported by the CBO have only been because the Repukes have refused to allow the tax revenue which is needed to pay for them - including for their own Republican constituents known as "values voters" (especially in the Deep South). They have even disallowed raising the payroll cap to \$1m, requiring more rich folks to pay in, which would immediately make Social Security viable for another 75 years. But they know if they did that, the current Generation X and Y'ers would also be assured of receiving their benefits so might well become long time program defenders - by becoming Dem voters!

Meanwhile, in a separate pragraph, the CBO validated this by noting that these current and future expenditures could be kept pace with provided the Bush tax cuts be allowed to expire next year and allow the AMT (alternative minimum tax) to hit higher income families. If not, according to the CBO, "under current tax policies, revenue will barely cover the cost of the health and retirement programs alone by 2035."

But again, this is what the GOP wants! They want to put the Democratic Party under severe political pressure,in any ways they can. Just as they're now doing it behind the scenes in many Repug-held states (by governorship) thus requiring strict photo IDs for any future voters (i.e. next year), which they know many of the elderly, African-American and young will never be able to meet.

Here's the dirty filthy truth these anti-tax miscreants don't want people to know: current tax rates as a percentage of GDP are the LOWEST they've been in nearly 40 years! The other dirty secret is that even without the military adventures and "wars" of choice, the Bush tax cuts themselves would've bled us into massive debt. The extended occupations, being unpaid for by higher taxes, just exacerbated the horrific debt ratio much more! The CBO in its report states if current tax rejection policies remain unchanged (and the national debt continues to grow as a result) then U.S. economic output could be as much as 6% smaller than current projections by 2018 and 18% by 2035.

This again, isn't startling or amazing! As early as 1995, economists James Medoff and Andrew Harless, in the The Indebted Society (p. 84, 'Let Them Eat Cake'), found that that "high tax rates are associated with higher productivity growth". There is a consistent and strong relationship. By contrast, for the years when supply side dogma held (during the Reagan and Bush Sr. years), productivity retreated by more than 30% and debt exploded- exactly the opposite of what we've been sold. As they wrote:

"For the health of the economy, Reagan's policies turned out to be just about the worst thing that could have happened: investment did not increase, growth continued to stagnate, and the federal deficit ballooned to new dimensions.

This was validated (for the Bush tax cuts, or as we call them, "Reagan Supply side II") by a Financial Times detailed analysis of the Bush Tax cuts in its Sept. 15, 2010 issue (page 24), wherein it was observed:

"“The 2000s- that is the period immediately following the Bush tax cuts – were the weakest decade in U.S. postwar history for real, non-residential capital investment. Not only were the 2000s by far the weakest period but the tax cuts did not even curtail the secular slowdown in the growth of business structures. Rather the slowdown accelerated to a full decline”

Contrast this with the hike in taxes (to only 39.5%) immediately after Bill Clinton took office, leading to the accumulation of more than \$600 billion in surpluses by the time he left in 2000, and the creation of 20 million jobs.

Meanwhile, the FT analysis observes that “during each decade from the 1950s to the 1990s, growth in real gross non-residential investment averaged between 3.5 percent and 7.4 percent a decade. During the 2000s it averaged a mere 1%”

It is evident to anyone but a certified idiot, that higher taxes are the path out of our financial morass. On the other hand, the continued stubbonr refusal to raise taxes is the path to national fiscal suicide and the U.S. rapidly becoming a very large third world country - with a few elites at the top, but the mass of people groveling.

THIS is why the GOP anti-tax position is not only dishonest and despicable, but fiscally traitorous as well. The Dems, for their part, must not yield to this extortion - no matter what threats the Repukes make! Or how many times Eric Kantor pitches a tantrum or Boner weeps his eyes out!

### Scoring President Obama

Barack Obama did a magnificent job in his speech two nights ago, in performing a flexible bit of political tap dancing that would make King Solomon proud in terms of splitting differences. In addition, he managed to upset the Whacko Right (which will always want tax cuts and indefinite military spending to weaken domestic safety nets) as well as the Left. How to score him? I gave him a 10 out of 10 for lucidity, but a 5 out of 10 for policy effect, including worsening the debt position-deficit over the next 3 1/2 years.

The sad and inescapable fact is that his decision to have only 10,000 leave the Afghan theater by the end of the year, and only 23,000 by the end of next year, merely brings us back to "square one". In other words, what we had before Mr. Obama's surge in 2009. This means at least a minimum of \$100 billion pissed down that rathole every year...until 2014, given now as the putative date for final clear out. That means by the end of it all, at least \$800 BILLION will have been squandered on a nation which is really in a Tribal Civil war while immense domestic needs (like infrastructure repair) go unattended. This is in addition to nearly \$3 trillion similarly squandered in Iraq. (Not including \$280 billion to pack & transport the expended -leftover materiel out of Iraq to Kuwait)

Between this fiasco and the extension of the Bush tax cuts in December, nearly \$1.7 trillion will have been added to the deficit - which we are to understand is now reaching a critical mass (though from the behavior of most politicos you'd never know it).

The Repukes are the worst hypocrites, in that on every TV appearance they're whining about the "deficit" this and that, yet refuse to do the ONE thing that will most effectively cut it: RAISE REVENUE via taxes! They believe, in their insipid little dwarf brains, they can actually cut the deficit by 40% merely via spending cuts. Are they insane? One believes so, but more on this in the next blog.

Given Obama's feeble draw down it's therefore passing crazy for the Reeps to be barking like rabid dogs about "betraying the generals" and our "fighting men". How about betraying all the citizens of this country, many of whom don't know where the next meal is coming from...or mortgage payment? How about allowing insane and wasteful spending to continue without even having the guts to at least pay for what you endorse, Reepos? How about the insanity of continuing a defense policy which in the end gets us nothing, because - make no mistake- Afghanistan will be what it is 3 years from now, and 33 years from now! Several empires and wannabes (the last the former Soviet Union) have already learned that to their eternal pain and sorrow!

And then we hear "the generals don't like it" or "hate it" or whatever! But who the fuck are the generals? The generals are NOBODY! It is the President who is Commander in Chief so it is HIS decisions that are to be followed! The "generals" - mainly the Joint Chiefs - will always want their little military escapades and interventions....hell, it keeps them in business and the \$\$\$ flowing to defense contractors! If the "generals" had their way we'd never have a moment's peace because their precious military-industrial complex would face de-funding. That's why departing Defense Secretary Robert Gates' words (concerning too large defense cuts making the U.S. military less capable) need to be taken with a grain of salt, as well as those of Gen David Petraeus.

John Fitzgerald Kennedy heard the same crap from his JCS when he held the highest office. Not only did those dicks want him to actually invade Cuba and bomb it during the Missile crisis in October, 1962,(which would have let all Hell loose) but Gen. Curtis LeMay compared him to Neville Chamberlain as an even "worse appeaser". Can you believe that? But JFK had the stones to stand his ground. Moreso in the case of Vietnam, when after assessing all the evidence in September, 1963 he then signed National Security Action Memorandum 263 to have all the troops out by calendar year 1965. The ARVN (South Vietnamese) were to take over ALL military functions by then, come hell or high water.

Of course the "generals" didn't like it. Not one bit! Their favorite bit of codswallop was the now discredited "domino theory". In fact, this was perhaps the most infamous slippery slope "argument"(actually a logical fallacy) of all, invoked to delay or prevent the U.S. departure from a losing effort in Viet Nam. LBJ bought into it, big time, which was why once he became President, his first act was to fire off NSAM-273 to repeal JFK's NSAM 263 draw down mandate. After that, he merely needed to engineer the right ruse to ramp up U.S. involvement and manpower, which he via the phoney Turner Joy and Maddox humbug incident in August, 1964.

But even after more than 10 years of bloody jungle war, the Reeps and their warmonger sidekicks (and Generals) kept yapping:

"Oh, we can’t leave, not now! Not at this time! If we just pull out Viet Nam will be the first of many dominoes to fall across Southeast Asia! Next will be Cambodia, then Thailand (Myanmar), then Laos, then Malaysia and who knows where it will end? The Philippines too?”

As it transpired, the depletion of treasure (\$269 billion) forced the U.S. to finally bail out in 1975, with over 58,000 American dead by that time. Whereas, the numbers would have been much less had fewer powerful minds not succumbed to the slippery slope “domino theory” nonsense.

Similar nonsense arguments have been enlisted to try to prevent the U.S. from leaving another military quagmire in Iraq. (Though to be sure, the cost in casualties is more by way of slow attrition and medical costs than from outright large battles like in ‘Nam). This time, the slippery slope is that if the U.S. leaves, the entire Middle East will fall to "terrorists". And after that, they will follow us home and attack us in our Malls. Now, since we can’t have that, it follows that we will have to stay in Iraq for generations! Problem is, where’s the money going to come from to pay for it? It's all very well to proclaim we'll be in those places indefinitely, but how many loans do you think the Chinese are going to make - especially with Bernanke's near zero interest rates?

Nobody seems to be able to address the money question, despite the fact in all previous serious interventions (such as WWII, Korea and Vietnam) taxes were raised to pay for their increasing costs - and/or the debts engendered in the aftermath. Now, all the reep-tards and their tea party idiots (who ought to be siding with Ron Paul to demand pullout)seem to believe two full bore occupations can be managed with TAX CUTS!

In the end, the real head-on combat is coming, in about 40 days, when the debt ceiling will need to be raised. The sad truth is, without all the military interventions of the past ten years - plus the insane and idiotic tax cuts- we wouldn't be anywhere near this predicament, nor would blow-dried pundits be bloviating about cutting "entitlements". The true fact was as former defense analyst Chuck Spinney put it back in 2004, the escalating military-defense budget has effectively caused a fiscal war to be waged on Medicare and Social Security.

One hopes Mr. Obama grasps this more securely the next time he gives a speech on Afghanistan!

## Thursday, June 23, 2011

### Introduction to Basic Physics (Lens combinations) Pt. 20

We now look at the practical combination of thin lenses which yields optical instruments such as the one shown in the accompanying photo of Caribbean science student Carson King, who won top price at a Science Exhibition with his self-designed and constructed 2" aperture refracting telescope (which he converted to an astro -camera to take photos of the Moon.)

The typical thin lens combo is shown in the illustrated example, asking 'Where is the final image?' The key step is to use the known focal lengths (f1 = 10 cm and f2 = 20 cm) and then perform the working as shown. The trick is to find the image distance s1' for the first lens, then having done that find the object distance s2 of the second lens. One can also obtain the total magnification (lateral) using the magnification formula.

We look at the procedure, then complete the solution for the converging lens system shown.

Procedure in analyzing a thin lens combination:

1) The image of the first lens (L1) is calculated as if the 2nd lens (L2) is not present.

2) The image of the first lens is treated as the object of the 2nd lens.

3) If the image of the first lens lies to the right of the 2nd lens, the image is treated as a virtual object for the 2nd lens (that is, s is negative). Refer again to the sign rules in the previous blog on lenses.

4) The image of the 2nd lens is the final image of the system.

Application:

Using the thin lens eqn. for lens L1:

1/s1 + 1/s1' = 1/15 + 1/s1' = 1/10 cm

therefore: s1' = 30 cm

e.g.: 1/ s1' = 1/15 - 1/10 = 5/150 or s1' = 150 cm/ 5

And for the 2nd lens:

1/s2 + 1/s2' = 1/f2

-> 1/ (-10 cm) + 1/s2' = 1/20 cm

or 1/s2' = 1/20 cm + 1/ 10 cm = 30 / 200 cm^-1 or s2' = 200/30 = (20/3) cm

Thus, the final image lies (20/3) cm to the right of the 2nd lens.

The lateral magnification for each lens is defined as before (see, e.g. solutions to previous problems):

M1 = (-s1'/ s1) = - (30 cm/ 15 cm) = -2

M2 = (-s2'/s2) = -(20/3)cm/ -10 cm = 2/3

Then the total magnification of the lens system is:

M1 M2 = (-2)(2/3) = -4/3

So it is:

real, inverted and enlarged by 4/3 times over the object.

In the case of the refracting telescope, such as shown in the photo, the magnifying power is defined by:

m = F/f(e)

where F is the focal length of the objective (the main or front lens) and f(e) is the focal length of the eyepiece. Hence, to get a large magnification one needs F to be fairly large and f(e) to be small.

Problems:

(1) A telephoto lens consists of a converging lens of focal length 6 cm placed 4 cm in front of a diverging lens of focal length (-2.5 cm).

a) Do a graphical construction of the system showing where the image would be.
b) Compare the size of the image formed by this combination with the size of the image that would be formed by the positive lens alone.

2) The objective lens of an astronomical telescope has a focal length of 6 ft. The eyepiece has a focal length of 2 inches.

a) Find the angular magnification that the telescope will produce when used for distant objects.

b) A rule for observing extended astronomical objects, such as planets or nebulae, is that the telescope magnification should not exceed 60x per inch of objective aperture.

If the astronomical telescope of this problem is used to observe the planet Jupiter,is the condition met or not? If not, what focal length eyepiece is needed to get the maximum angular magnification?

3) The objective of a telescope has a focal length F = 30 in. When it is used for an object at a great distance, then the distance between the objective and eyepiece is 32 in. What is the angular magnification?